Abstract: The computational potential of a quantum processor can only be unleashed if errors during a quantum computation can be controlled and corrected for. Quantum error correction works if imperfections of quantum gate operations and measurements are below a certain threshold and corrections can be applied repeatedly. We implement multiple quantum error correction cycles for phase-flip errors on qubits encoded with trapped ions. Errors are corrected by a quantum-feedback algorithm using high-fidelity gate operations and a reset technique for the auxiliary qubits. Up to three consecutive correction cycles are realized, and the behavior of the algorithm for different noise environments is analyzed.

Abstract: The generation, manipulation and detection of quantum bits (qubits) encoded on single photons is at the heart of quantum communication and optical quantum information processing. The combination of single-photon sources, passive optical circuits and single-photon detectors enables quantum repeaters and qubit amplifiers, and also forms the basis of all-optical quantum gates and of linear-optics quantum computing. However, the monolithic integration of sources, waveguides and detectors on the same chip, as needed for scaling to meaningful number of qubits, is very challenging, and previous work on quantum photonic circuits has used external sources and detectors. Here we propose an approach to a fully-integrated quantum photonic circuit on a semiconductor chip, and demonstrate a key component of such circuit, a waveguide single-photon detector. Our detectors, based on superconducting nanowires on GaAs ridge waveguides, provide high efficiency (20%) at telecom wavelengths, high timing accuracy (60 ps), response time in the ns range, and are fully compatible with the integration of single-photon sources, passive networks and modulators.

Abstract: Large-scale quantum computation will only be achieved if experimentally implementable quantum error correction procedures are devised that can tolerate experimentally achievable error rates We describe an improved decoding algorithm for the Kitaev surface code, which requires only a two-dimensional square lattice of qubits that can interact with their nearest neighbors, that raises the tolerable quantum gate error rate to over 1% The precise maximum tolerable error rate depends on the error model, and we calculate values in the range 11--14% for various physically reasonable models These values represent a very high threshold error rate calculated in a constrained setting

Abstract: In quantum computation every unitary operation can be decomposed into quantum circuits---a series of single-qubit rotations and a single type entangling two-qubit gates, such as controlled-not(cnot) gates. Two measures are important when judging the complexity of the circuit: the total number of cnot gates needed to implement it and the depth of the circuit, measured by the minimal number of computation steps needed to perform it. Here we give an explicit and simple quantum circuit scheme for preparation of arbitrary quantum states, which can directly utilize any decomposition scheme for arbitrary full quantum gates, thus connecting the two problems. Our circuit reduces the depth of the best currently known circuit by a factor of $2$. It also reduces the total number of cnot gates from ${2}^{n}$ to $\frac{23}{24}{2}^{n}$ in the leading order for even number of qubits. Specifically, the scheme allows us to decrease the upper bound from $11$ cnot gates to $9$ and the depth from $11$ to $5$ steps for four qubits. Our results are expected to help in designing and building small-scale quantum circuits using present technologies.

Abstract: We develop a non-adiabatic generalization of holonomic quantum computation in which high-speed universal quantum gates can be realized by using non-Abelian geometric phases. We show how a set of non-adiabatic holonomic one- and two-qubit gates can be implemented by utilizing optical transitions in a generic three-level $\Lambda$ configuration. Our scheme opens up for universal holonomic quantum computation on qubits characterized by short coherence times.

Abstract: Logic gates can be performed on data encoded in quantum code blocks such that errors introduced by faulty gates can be corrected. The important class of transversal gates acts bitwise between corresponding qubits of code blocks and thus limits error propagation. If any quantum gate could be implemented using transversal gates, the set would be universal. We study the structure of GF(4)-additive quantum codes and prove that no universal set of transversal logic gates exists for these codes. This result is in stark contrast with the classical case, where universal transversal gate sets exist, and strongly supports the idea that additional quantum techniques, based, for example, on quantum teleportation or magic state distillation, are necessary to achieve universal fault-tolerant quantum computation on additive codes.

Abstract: We show that a chemically engineered structural asymmetry in [Tb2] molecular clusters renders the two weakly coupled Tb3+ spin qubits magnetically inequivalent. The magnetic energy level spectrum of these molecules meets then all conditions needed to realize a universal CNOT quantum gate. A proposal to realize a SWAP gate within the same molecule is also discussed. Electronic paramagnetic resonance experiments confirm that CNOT and SWAP transitions are not forbidden.

Abstract: Optimal control methods for implementing quantum modules with least amount of relaxative loss are devised to give best approximations to unitary gates under relaxation. The potential gain by optimal control fully exploiting known relaxation parameters against time-optimal control (the alternative for unknown relaxation parameters) is explored and exemplified in numerical and in algebraic terms: for instance, relaxation-based optimal control is the method of choice to govern quantum systems within subspaces of weak relaxation whenever the drift Hamiltonian would otherwise drive the system through fast decaying modes. In a standard model system generalizing ideal decoherence-free subspaces to more realistic scenarios, opengrape-derived controls realize a CNOT with fidelities beyond 95% instead of at most 15% for a standard Trotter expansion. As additional benefit their control fields are orders of magnitude lower in power than bang-bang decouplings.

Abstract: We study how dynamical decoupling (DD) pulse sequences can improve the reliability of quantum computers. We prove upper bounds on the accuracy of DD-protected quantum gates and derive sufficient conditions for DD-protected gates to outperform unprotected gates. Under suitable conditions, fault-tolerant quantum circuits constructed from DD-protected gates can tolerate stronger noise and have a lower overhead cost than fault-tolerant circuits constructed from unprotected gates. Our accuracy estimates depend on the dynamics of the bath that couples to the quantum computer and can be expressed either in terms of the operator norm of the bath’s Hamiltonian or in terms of the power spectrum of bath correlations; we explain in particular how the performance of recursively generated concatenated pulse sequences can be analyzed from either viewpoint. Our results apply to Hamiltonian noise models with limited spatial correlations.

Abstract: In quantum information processing, it is vital to protect the coherence of qubits in noisy environments. Dynamical decoupling (DD), which applies a sequence of flips on qubits and averages the qubit-environment coupling to zero, is a promising strategy compatible with other desired functionalities, such as quantum gates. Here, we review the recent progresses in theories of dynamical decoupling and experimental demonstrations. We give both semiclassical and quantum descriptions of the qubit decoherence due to coupling to noisy environments. Based on the quantum picture, a geometrical interpretation of DD is presented. The periodic Carr-Purcell-Meiboom-Gill DD and the concatenated DD are reviewed, followed by a detailed exploration of the recently developed Uhrig DD, which employs the least number of pulses in an unequally spaced sequence to suppress the qubit-environment coupling to a given order of the evolution time. Some new developments and perspectives are also discussed.

Abstract: Optimal control theory is a versatile tool that presents a route to significantly improving figures of merit for quantum information tasks. We combine it here with the geometric theory for local equivalence classes of two-qubit operations to derive an optimization algorithm that determines the best entangling two-qubit gate for a given physical setting. We demonstrate the power of this approach for trapped polar molecules and neutral atoms.

Abstract: In [1] we have presented the reversible subtractor designs based on a new reversible TR gate (TR refers to Thapliyal Ranganathan). In [1] as the quantum gates implementation of the TR gate was not known, only the upper bound on the quantum cost of the reversible subtractors units were established. In this work, we present a new design of the reversible half subtractor based on the quantum gates implementation of the reversible TR gate. The reversible TR gate is designed from 2×2 quantum gates such as CNOT and Controlled-V and Controlled-V+ gates. The design of the proposed reversible half subtractor is shown to be better than the design presented in [2], [1] in terms of the quantum cost and delay while maintaining the minimum number of garbage outputs. Further, we present a new design of the reversible full subtractor based on the proposed quantum gates implementation of the TR gate. The proposed reversible full subtractor is optimized in terms of quantum cost, delay and garbage outputs by utilizing the identity property of V and V+ reversible gates. The proposed reversible full subtractor is shown to be better than the existing design reported in [3], [1]. The reversible subtractors proposed in this work will be useful in a number of digital signal processing applications.

Abstract: Constructing appropriate unitary matrix operators for new quantum algorithms and finding the minimum cost gate sequences for the implementation of these unitary operators is of fundamental importance in the field of quantum information and quantum computation. Evolution of quantum circuits faces two major challenges: complex and huge search space and the high costs of simulating quantum circuits on classical computers. Here, we use the group leaders optimization algorithm to decompose a given unitary matrix into a proper-minimum cost quantum gate sequence. We test the method on the known decompositions of Toffoli gate, the amplification step of the Grover search algorithm, the quantum Fourier transform, and the sender part of the quantum teleportation. Using this procedure, we present the circuit designs for the simulation of the unitary propagators of the Hamiltonians for the hydrogen and the water molecules. The approach is general and can be applied to generate the sequence of quantum gates for larger molecular systems.

Abstract: We experimentally demonstrate a controlled-phase gate for continuous variables using a cluster-state resource of four optical modes. The two independent input states of the gate are coupled with the cluster in a teleportation-based fashion. As a result, one of the entanglement links present in the initial cluster state appears in the two unmeasured output modes as the corresponding entangling gate acting on the input states. The genuine quantum character of this gate becomes manifest and is verified through the presence of entanglement at the output for a product two-mode coherent input state. By combining our gate with the recently reported module for single-mode Gaussian operations [R. Ukai et al., Phys. Rev. Lett. 106, 240504 (2011)], it is possible to implement any multimode Gaussian operation as a fully measurement-based one-way quantum computation.

Abstract: Linear Nearest Neighbor (LNN) synthesis in reversible circuits has emerged as an important issue in terms of technological implementation for quantum computation. The objective is to obtain a LNN architecture with minimum gate cost. As achieving optimal synthesis is a hard problem, heuristic methods have been proposed in recent literature. In this work we present a graph partitioning based approach for LNN synthesis with reduction in circuit cost. In particular, the number of SWAP gates required to convert a given gate-level quantum circuit to its equivalent LNN configuration is minimized. Our algorithm determines the reordering of indices of the qubit line(s) for both single control and multiple controlled gates. Experimental results for placing the target qubits of Multiple Controlled Toffoli (MCT) library of benchmark circuits show a significant reduction in gate count and quantum gate cost compared to those of related research works.

Abstract: We report on the first experimental realization of optimal linear-optical controlled phase gates for arbitrary phases. The realized scheme is entirely flexible in that the phase shift can be tuned to any given value. All such controlled phase gates are optimal in the sense that they operate at the maximum possible success probabilities that are achievable within the framework of postselected linear-optical implementations with vacuum ancillas. The quantum gate is implemented by using bulk optical elements and polarization encoding of qubit states. We have experimentally explored the remarkable observation that the optimum success probability is not monotone in the phase.

Abstract: Mapping a circuit of reversible gates to a circuit of elementary quantum gates is a key step in synthesizing quantum realizations of Boolean functions. The library containing NOT, controlled-NOT and controlled square-root-of-NOT gates has been considered extensively. In this paper, we extend the library to include fourth-root-of-NOT gates. Experimental results using REVLIB benchmark circuits show that using this extended library results in smaller quantum circuits.

Abstract: We study the implementation of one-, two-, and three-qubit quantum gates for interacting qubits using optimal control. Different Markovian and non-Markovian environments are compared and efficient optimisation algorithms utilising analytic gradient expressions and quasi-Newton updates are given for both cases. The performance of the algorithms is analysed for a large set of problems in terms of the fidelities attained and the observed convergence behaviour. New notions of success rate and success speed are introduced and density plots are utilised to study the effect of key parameters, such as gate operation times, and random variables, such as the initial fields required to start the iterative algorithm. Core characteristics of the optimal fields are statistically analysed. Substantial differences between Markovian and non-Markovian environments in terms of the possibilities for control and the control mechanisms are uncovered. In particular, in the Markovian case it is found that the optimal fields obtained without considering the environment cannot be improved substantially by taking the environment into account and the fidelities attained are determined mostly by the gate operation time as well as the overall strength of the environmental effects. Computation time is saved if the fields are pre-optimised neglecting decoherence. In the non-Markovian case, on the other hand, substantial improvements in the fidelities are observed when the details of the system-bath coupling are taken into account. In that case, field leakage is shown to be a significant issue which can make high gate fidelities impossible to obtain unless both the system and noise qubits are fully controlled.

Abstract: We realize quantum gates for path qubits with a high-speed, polarization-independent and tunable beam splitter. Two electro-optical modulators act in a Mach-Zehnder interferometer as high-speed phase shifters and rapidly tune its splitting ratio. We test its performance with heralded single photons, observing a polarization-independent interference contrast above 95%. The switching time is about 5.6 ns, and a maximal repetition rate is 2.5 MHz. We demonstrate tunable feed-forward operations of a single-qubit gate of path-encoded qubits and a two-qubit gate via measurement-induced interaction between two photons.

Abstract: Experiments performed within the last year have demonstrated Rydberg state mediated quantum gates and deterministic entanglement between pairs of trapped neutral atoms. These experiments validate ten year old proposals for Rydberg mediated quantum logic, but are only the beginning of ongoing efforts to improve the fidelity of the results obtained and scale the experiments to larger numbers of qubits. We present here a summary of the results to date, along with a critical evaluation of the prospects for higher fidelity Rydberg gates.

Abstract: Quantum information processing requires overcoming decoherence—the loss of ‘quantumness’ due to the inevitable interaction between the quantum system and its environment. One approach towards a solution is quantum dynamical decoupling—a method employing strong and frequent pulses applied to the qubits. Here we report on the first experimental test of the concatenated dynamical decoupling (CDD) scheme, which invokes recursively constructed pulse sequences. Using nuclear magnetic resonance, we demonstrate a near order of magnitude improvement in the decay time of stored quantum states. In conjunction with recent results on high fidelity quantum gates using CDD, our results suggest that quantum dynamical decoupling should be used as a first layer of defense against decoherence in quantum information processing implementations, and can be a stand-alone solution in the right parameter regime.

Abstract: While several physical realization schemes have been proposed for future quantum information processing, most known facts suggest that quantum information processing should have intrinsic limitations; physically realizable operations would be only interaction between neighbor qubits. To use only such physically realizable operations, we need to convert a general quantum circuit into one for an so-called Linear Nearest Neighbor (LNN) architecture where any gates should be operated between only adjacent qubits. Thus, there has been much attention to develop efficient methods to design quantum circuits for an LNN architecture. Most of the existing researches do not consider changing the gate order of the original circuit, and thus the result may not be optimal. In this paper, we propose a method to convert a quantum circuit into one for an LNN architecture with the smallest number of SWAP gates. Our method improves the previous result for Approximate Quantum Fourier Transform (AQFT) by the state-of-the-art design method.

Abstract: Exchange-coupled singlet-triplet spin qubits in two gate-defined double quantum dots are considered theoretically. Using charge density operators to describe the double-dot orbital states, we calculate the Coulomb couplings between the qubits, and identify optimal bias points for single- and two-qubit operations, as well as convenient idle positions. The same intuitive formulation is used to derive dephasing rates of these qubits due to the fluctuating charge environment, thereby providing the main considerations for a quantum computation architecture that is within current experimental capabilities.

Abstract: We present a logic synthesis method based on lattices that realize quan- tum arrays in One-Dimensional Ion Trap technology. This means that all gates are built from 2x2 quantum primitives that are located only on neighbor qubits in a one- dimensional space (called also vector of qubits or Linear Nearest Neighbor (LNN) architecture). The Logic circuits designed by the proposed method are realized only with 3*3 Toffoli, Feynman and NOT quantum gates and the usage of the commonly used multi-input Toffoli gates is avoided. This realizatio n method of quantum cir- cuits is different from most of reversible circuits synthes is methods from the literature that use only high level quantum cost based on the number of quantum gates. Our synthesis approach applies to both standard and LNN quantum cost models. It leads to entirely new CAD algorithms for circuit synthesis and substantially decreases the quantum cost for LNN quantum circuits. The drawback of synthesizing circuits in the presented LNN architecture is the addition of ancilla qubits.

Abstract: reference frames simplify the implementation of single qubit gates by avoiding the necessity of correcting phase shifts (z-rotations), but also provide a simple way of implementing desired z-rotations. Rotating the frame instead of the spin is simply a matter of computational book keeping, and so can in principle be done instantaneously and perfectly. For this reason it is often sensible to decompose single-qubit gates into circuits involving z-rotations wherever possible. One important example is the Hadamard gate, Eq. 19, which can be implemented using the pulse sequence 90−y 180z or equivalently 180z 90y. The z-rotations can be absorbed into the reference frame, and so Hadamard gates can be replaced by h = 90y, sometimes called the pseudo-Hadamard gate [12,19], or its inverse, h−1 = 90−y. As Hadamard gates frequently occur in pairs, these pairs can be replaced by one h−1 and one h gate, with the 180z rotations cancelling out; when they do not occur in pairs it is still possible to replace them with pseudo-Hadamard gates as long as the 180z rotations are absorbed into the reference frames. An alternative approach which has grown in popularity is to use methods from optimal control theory to develop shaped pulses which both provide selective excitation and refocus undesirable interactions. This approach is explored in more detail in Section 3.7 below. 3.3 Basic methods: controlled gates Next I turn to non-trivial two-qubit gates, and will begin by considering twospin (two-qubit) systems. It is in principle only necessary to construct a single gate of this kind, and the traditional gate used in most theoretical descriptions is the controlled-not gate, or controlled-X gate, Eq. 23. In NMR experiments, however, the key two-qubit gate is the controlled-Z gate

Abstract: Systems and methods are provided for performing a quantum gate operation. A first classical control parameter is associated with a first qubit and coupled to a resonator. The first classical control parameter is transitioned from a first control value to a second control value. The first classical control parameter is returned from the second control value to the first control value via an adiabatic sweep operation, as to permit a transfer of energy between the first qubit and the resonator that causes a change in the quantum state of the qubit and resonator.

Abstract: Photons are ideal carriers of quantum information over long distances. It is interesting to explore their potential for the implementation of quantum information processing as well. This is particularly relevant for quantum repeaters [1–3], which would allow one to distribute quantum states over distances that are inaccessible by direct transmission. Quantum repeaters require both the capability to store photons for relatively long times and to perform efficient quantum gates between them [3]. Potential architectures where storage and quantum gates can be achieved in the same system are particularly attractive. Recently it was shown that light can be stored for over a second in a Bose-Einstein condensate (BEC) [4], making condensates a very interesting candidate system for the implementation of quantum memories. Quantum repeaters can tolerate long gate times in the sub-second range, since repetition rates are in any case limited by other factors such as communication times and transmission probabilities. It is therefore of great interest to explore the potential for photon-photon gates in BECs, where interactions between stored excitations are weak, but non-zero. In the following we describe a concrete proposal for realizing such photon-photon gates in BECs. Our work builds on Refs. [5, 6], but we focus on the case of two single photons interacting. In this extremely low-intensity regime achieving significant controlled phase shifts is not straightforward. However, we show that phase shifts of � can be achieved on sub-second timescales by combining a Feshbach enhancement of the relevant scattering length and an adiabatic compression of the trap after the light has been stored. The fidelity of photon-photon gates can be affected by unwanted multi-mode effects, see e.g. Ref. [7]. In the present proposal these effects are greatly suppressed by the fact that the interaction is much weaker than the confinement, ensuring high-fidelity operations. Let us assume that the two photons have orthogonal polarization. Their propagation inside the BEC can be controlled by two independent control beams, leading to storage in two different atomic levels 1 and 2, where the BEC was prepared in level 0, see Fig. 1. Slow and stopped light in BECs has been thoroughly investigated [4, 5, 8–10]. Due to the linearity of the equations of motion, the physics of storage and retrieval is the same at FIG. 1: Level scheme for photon-photon gate. The BEC is prepared in level 0. The single photons in modes E1 and E2 can be independently stored as delocalized excitations in levels 1 and 2, using the control beams 1 and 2.

Abstract: Reversible logic gates have attracted significant attention to the researchers in the field of optics and optoelectronics as it has wide applications in sequential and combinational circuit of optical computing, optical signal processing and in multi-valued logic operations. Several all-optical reversible logic gates have been proposed such as controlled NOT (Feynman gate), Fredkin gate, Toffoli gate, New Gate, Peres gate etc. The beauty of all these reversible conservative logic gates is that all types of arithmetic and logical operation can be performed with these gates with lower hardware complexity and without loss of any input information. To perform these logic operations, encoding and decoding of optical signals are of great important issues. In this communication the author presents a method of designing all optical Fredkin gate and Toffoli gate using frequency encoding/decoding techniques because of several inherent advantages of this encoding/decoding. To develop the method of designing these two reversible logic gates, non-linear polarisation rotation of the probe beam, frequency routing and frequency conversion properties of semiconductor optical amplifiers have been exploited which will give very high operational speed (of the order of THz) with very good on/off contrast ratio.